Intro

Hello and Welcome to this episode of the podcast, "The Mnemonic Tree", where we add a single mnemonic leaf, to our Tree of Knowledge.

Today's episode has been a real enlightenment of learning for me, as I don’t think I ever fully understood all the intricacies of the order of operation, vis-a-vis BODMAS or PEMDAS.

Some may ask, how do you have a rule of operation and the two mnemonics BODMAS and PEMDAS are spelt differently. How does that work? Well, fair question, and I hope by the end of this episode that becomes clear, along with a basic understanding of this critical function and its prolific use in mathematics and computing.

So, with no further ado, we will begin with a summary from Wikipedia.

https://commons.wikimedia.org/wiki/File:Order_of_operations.svg

Wikipedia Summary

In mathematics and computer programming, the order of operations (or operator precedence) is a collection of rules that reflect conventions about which procedures to perform first in order to evaluate a given mathematical expression.

For example, in mathematics and most computer languages, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation.[1][2] Thus, the expression 1 + 2 × 3 is interpreted to have the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication, and could be placed only as a superscript to the right of their base.[1] Thus 3 + 52 = 28 and 3 × 52 = 75.

These conventions exist to eliminate notational ambiguity, while allowing notation to be as brief as possible. Where it is desired to override the precedence conventions, or even simply to emphasize them, parentheses ( ) can be used. For example, (2 + 3) × 4 = 20 forces addition to precede multiplication, while (3 + 5)2 = 64 forces addition to precede exponentiation. If multiple pairs of parentheses are required in a mathematical expression (such as in the case of nested parentheses), the parentheses may be replaced by brackets or braces to avoid confusion, as in [2 × (3 + 4)] − 5 = 9.

BODMAS

1. (mathematics, mnemonic) An acronym for the arithmetic order of precedence, with the highest precedence first: Brackets, order, division, multiplication, addition, subtraction

Extracted from: [https://en.wikipedia.org/wiki/Order_of_operations]

https://commons.wikimedia.org/wiki/File:Order1.gif

Mnemonic

Order of Operations – Mathematics & Computer Programming – BODMAS

(Picture taking your body mass index which is your weight divided by your height squared)

1. Brackets

2. Order

3. Division

4. Multiplication

5. Addition

6. Subtraction

Five Fun Facts

1. The mathematician who invented the mnemonic BODMAS was Achilles Reselfelt. I’d love to tell you what country he came from and when he was born but unbelievably, I cannot find a thing on this mysterious man. If anyone out there knows anything about this man, please shoot me an email through the website or straight to themnemonictree@gmail.com and I can let everyone know on the next episode.

2. The next question would be then, when was the BODMAS rule invented? And again, disappointingly there is no definitive date for the invention of BODMAS but it appeared in writing around the early 1600’s. The rules were not seen until the development of algebraic notation.

Now just speaking of Algebra, I once had an algebra teacher who was actually afraid of negative numbers? Dare I say, he’d stop at nothing to avoid them! He did however have a good sense of humour and told us a great joke one day which was: “Why is six afraid of seven? Because seven eight nine!”

3. BODMAS has a twin brother called PEMDAS. The mnemonic PEMDAS stands for parenthesis, exponents, multiplication, division, addition and subtraction. As you would have noticed the multiplication comes before division as opposed to BODMAS, but never mind, this won’t affect the result as you do them in the order in which they come in the equation.

4. Another minor difference between BODMAS and PEMDAS is the O in BODMAS and the E in PEMDAS. As stated in the mnemonic O is order and in PEMDAS the E is exponents, but what do they mean? Well, order and exponents refer to powers and square roots, etc.

5. Finally, in regards to exponents. What if there is more than one exponent? Well, if there is, you start from the top and work your way down. For example:

Start with: 432 32 = 3×3 = 9 49 = 4×4×4×4×4×4×4×4×4 = 262,144

https://commons.wikimedia.org/wiki/File:%D8%AA%D9%82%D8%AF%D9%85_%D8%A7%D8%B9%D9%85%D8%A7%D9%84_%D8%B3%D9%87.gif

Three Question Quiz

Q.1. Calculate the following using the order of operation. 46 – (19+11)

Q.2. True or false: Addition always comes before subtraction?

Q.3. Calculate the following using the order of operation. 10 x 10 + 18 / 6

Bonus Q. What operation comes first in the following equation? (8 x 7 + 4) /30

Mnemonic Recap

Order of Operations – Mathematics & Computer Programming – BODMAS

(Picture taking your body mass index which is your weight divided by your height squared)

1. Brackets

2. Order

3. Division

4. Multiplication

5. Addition

6. Subtraction

Three Question Quiz Answers

Q.1. Calculate the following using the order of operation. 46 – (19+11)

A. 16

Q.2. True or false: Addition always comes before subtraction?

A. False. Remember, addition and subtraction are on the same algebraic operations priority level and you do them in the order in which they come in the equation

Q.3. Calculate the following using the order of operation. 10 x 10 + 18 / 6

A. 103

Bonus Q. What operation comes first in the following equation? (8 x 7 + 4) /30

A. Multiplication, because it’s inside the parenthesis and comes before addition. Answer is 2

Word of the Week

oppugn

[ uh-pyoon ]

verb

to assail by criticism, argument, or action.

Example

While researching this topic I have noticed that many people still oppugn as to the order of multiplication and division in the order of operation.

Extracted from: [https://www.dictionary.com/]